인공신경망(ANN)을 이용한 옵션가격결정 및 딥헤징 (DH)에 대한 SNN 및 RNN 결과의 비교·분석

Abstract

The purpose of this study is to present alternative methods to overcome market limitations such as the assumption of fixing the dynamics of underlying assets and market friction for the traditional Black-Scholes option pricing model. As for the research method of this paper, Adam is used as the gradient descent optimizer for the hedging model of the call option short portfolio using artificial neural network models SNN (simple neural network) and RNN (recurrent neural network) as analysis models, and deep neural network (deep neural network) is used as the hedging model. neural network) methodology was applied.
 The research results of this paper are as follows. Regarding the ATM call option price, the BS model showed 10.245, the risk neutral model showed 10.268, the SNN-DH model showed 11.834, and the RNN-DH model showed 11.882. Therefore, it appears that there is a slight difference in the call option price according to each analysis model. At this time, the DH analysis data sample is 100,000 (1×) training samples generated by Monte Carlo Simulation, and the number of testing samples is the training sample. 20% (20,000 pieces) was used, and the option payoff function is lambda(), which is -max(, 0). In addition, the option price and P&L (P&L) of SNN-DH and RNN-DH appear linearly on the basis, and the longer the remaining maturity, the closer the delta value of SNN-DH and BS to the distribution of the S-curve, and the closer the expiration date, the closer the two models are. Delta is densely distributed between 0 and 1. As for the total loss of delta hedging of the short call option position, SNN-DH was -0.0027 and RNN-DH was -0.0061, indicating that the total hedged profit and loss was close to 0.
 The implications of this study are to present DL techniques based on AI methods as an alternative way to overcome limitations such as fixing underlying asset dynamics and market friction of the traditional Black-Scholes model. In addition, it is an independent analysis model that considers valid robust tools by applying deep neural network algorithms for portfolio hedging problems. One limitation of the research is that it analyzed the model under the assumption of zero transaction costs, so future studies should consider this aspect.